1. Field of the Invention
The preferred embodiments of present invention relate to, among other things, methods for selecting one or more portfolio of tangible or intangible assets subject to optimization. The preferred embodiments provide a portfolio optimizer that enables investment managers to construct portfolios to meet targeted objectives.
2. Discussion of the Background
Managers of assets, such as portfolios of stocks and/or other assets, often seek to maximize returns on an overall investment, such as, e.g., for a given level of risk as defined in terms of variance of return, either historically or as adjusted using known portfolio management techniques.
Following the seminal work of Harry Markowitz in 1952, mean-variance optimization has been a common tool for portfolio selection. A mean-variance efficient porfolio can be constructed through an optimizer with inputs from an appropriate risk model and an alpha model. Such a portfolio helps ensure higher possible expected returns (e.g., net of taxes and subject to various constraints) for a given level of risk.
Risk lies at the heart of modern portfolio theory. The standard deviation (e.g., variance) of an asset's rate of return is often used to measure the risk associated with holding the asset. However, there can be other suitable or more suitable measures of an asset's risk than its standard deviation of return. A common definition of risk is the dispersion or volatility of returns for a single asset or porfolio, usually measured by standard deviation. With reference to U.S. Provisional Application Ser. No. 60/418,727 filed on Oct. 17, 2002, the disclosure of which is incorporated herein by reference in its entirety, ITG, Inc., the assignee of the present invention has developed a set of risk models for porfolio managers and traders to measure, analyze and manage risk in a rapidly changing market. These models can be used to, among other things, create mean-variance efficient portfolios in combination with a portfolio optimizer, such as, e.g., those set forth herein.
According to modern portfolio theory, for any portfolio of assets (such as, e.g., stocks and/or other assets) there is an efficient frontier, which represents variously weighted combinations of the portfolio's assets that yield the maximum possible expected return at any given level of portfolio risk.
In addition, a ratio of return to volatility that can be useful in comparing two portfolios in terms of risk-adjusted return is the Sharpe Ratio. This ratio was developed by Nobel Laureate William Sharpe. Typically, a higher Sharpe Ratio value is preferred. A high Sharpe ratio implies that a portfolio or asset (e.g., stock) is achieving good returns for each unit of risk. The Sharpe Ratio can be used to compare different assets or different portfolios. Often, it has been calculated by first subtracting the risk free rate from the return of the portfolio, and then dividing by the standard deviation of the portfolio. The historical average return of an asset or portfolio can be extremely misleading, and should not be considered alone when selecting assets or comparing the performance of portfolios. The Sharpe Ratio can allows one to factor in the potential impact of return volatility on expected return, and to objectively compare assets or portfolios that may vary widely in terms of returns.
By connecting a portfolio to a single risk factor, Sharpe simplified Markowitz's work. Sharpe developed a heretical notion of investment risk and reward—a sophisticated reasoning that has become known as the Capital Asset Pricing Model (CAPM). According to the CAPM, every investment carries two distinct risks. One is the risk of being in the market, which Sharpe called systematic risk. This risk, later dubbed “beta,” cannot be diversified away. The other risk, unsystematic risk, is specific to a company's fortunes. This uncertainty can be mitigated through appropriate diversification. Sharpe discerned that a portfolio's expected return hinges solely on its beta—its relationship to the overall market. The CAPM helps measure portfolio risk and the return an investor can expect for taking that risk.
Portfolio optimization often involves the process of analyzing a portfolio and managing the assets within it. Typically, this is done to obtain the highest return given a particular level of risk. Portfolio optimization can be conducted on a regular, periodic basis, such as, e.g., monthly, quarterly, semi-annually or annually might be sufficient. However, since one is not required to rebalance a portfolio each time one optimizes, one can optimize as frequently as desired. In considering rebalancing decisions, one typically also considers tax and/or transaction cost implications of selling some assets and buying other asssets as one pursues an optimal portfolio.
In some existing portfolio optimizers, techniques such as hill climbing or linear/quadratic programming are used to seek an optimal solution. With these systems, issues like long/short, minimum position size or position count constraints, tax costs and transaction costs generally cannot be modeled accurately using these techniques. In addition, U.S. Pat. No. 6,003,018, entitled Portfolio Optimization By Means Of Resampled Efficient Frontiers, the entire disclosure of which is incorporated herein by reference shows other optimizer methods. The present invention provides substantial improvement over these and other optimizers.
The present assignee has developed a portfolio optimizer, the ITG/Opt™ optimizer, that uses mixed integer programming (MIP) technology to produce more accurate results. The ITG/Opt™ optimizer provides enhanced results when, e.g., creating or rebalancing portfolios. The ITG/Opt optimizer performs optimization in one pass, with all constraints and parameters taken into account simultaneously. Any security characteristic can be constrained or introduced. In addition, a full range of portfolio characteristics may also be specified, including constraints on leverage, turnover, long vs. short positions, and more. Furthermore, constraints may be applied to an entire portfolio or to its long or short sides alone. Furthermore, the ITG/Opt avoids misleading heuristics by combining a branch-and-bound algorithm with objective scoring of potential solutions, reducing the size of the problem without damaging the integrity of the outcome.
Additionally, the ITG/Opt optimizer can accurately model the tax code. For example, integer modeling of tax brackets and tax lots enables the ITG/Opt optimizer to minimize net tax liability without discarding large blocks of profitable shares. The ITG/Opt is also adaptable to HIFO, LIFO, or FIFO accounting methods. In addition, the ITG/Opt is configured toward real-world complexities of sophisticated investment strategies. The ITG/Opt optimizer can handle complex and/or non-linear issues that arise in real-world fund management.
Additionally, the ITG/Opt optimizer can factor transaction costs resulting from market impact into its solutions. The optimizer includes a cost model, ACE™, for forecasting market impact. The inclusion of ACE enables users to weigh implicit transaction costs along with risks and expected returns of optimization scenarios.
Additionally, the ITG/Opt does effective historical back-testing. The ITG/Opt can closely track portfolios through time, accounting for the effects of splits, dividends, mergers, spinoffs, bankruptcies and name changes as they occur.
Additionally, the ITG/Opt is equipped to handle many funds and many users. The ITG/Opt system includes multiuser, client-server relational database management technology having the infrastructure to accommodate the demands of many simultaneous users and a large volume of transactions.
Additionally, the ITG/Opt integrates neatly with trade-order management and accounting systems. Because the ITG/Opt system is built on relational database management technology it is easy to link with other databases. The ITG/Opt can also generate trade lists for execution by proprietary TOM systems. Moreover, ITG/Opt's flexible design allows for extensive customization of reports to fit a companyies' operations and clients' needs. Moreover, custom report formats can be designed quickly and cost-effectively.
While a variety of portfolio optimization systems and methods may exist, there is a significant need in the art for systems and processes that improve upon the above and/or other systems and processes.